An air strike by the US-led coalition has "disabled" the fourth bridge over the River Tigris in Mosul, leaving the northern Iraqi city with just one functioning bridge.

The air strike further disrupts IS supply lines amid the government offensive against the militants.

The extremist group's media arm, the Aamaq news agency, and a top Iraqi commander in Mosul reported the air strike, which took place before dawn.

It was the second air strike to target a Mosul bridge this week and the fourth since shortly before the October 17 start of the Iraqi government's campaign to retake the city from IS.

The air strike was followed by intense fighting in an eastern Mosul neighbourhood where Iraq's special forces are slowly advancing toward the city centre, hampered by suicide car bombings, sniper fire and concerns over the safety of civilians still living inside the city.

Mosul had five bridges over the Tigris until shortly before the start of the campaign. Targeting the bridges appears designed to disrupt IS supply lines in Mosul, which is sliced in half by the river. Most of the fighting in Mosul is taking place in the eastern part of the city - east of the Tigris - where Iraqi special forces are slowly moving towards the city centre in the face of stiff IS resistance.

The destruction of the bridges means that the Iraqi military and its allies - the Kurdish peshmerga forces and Sunni tribesmen - would have to use military pontoon bridges to cross the river when they arrive at its banks.

Brigadier General Haider Fadhil, of the Iraqi special forces, said that his men were slowly pushing back IS fighters in the densely populated Mosul neighbourhood of Zohour. He said their progress was hampered by IS suicide car bombs, several of which were targeted by coalition aircraft before they reached their intended targets. His men were in control of about half the neighbourhood by Wednesday afternoon, he said.

Mortars, artillery and automatic fire were used in the fighting, which prompted dozens of families to flee their homes to the safety of centres set up for displaced civilians away from front-line neighbourhoods, according to reports. Unmanned aircraft flew overhead and deep booms from air strikes could be heard. Plumes of smoke rose above the battlefield.

By the afternoon, reinforcement of about 100 heavily armed special forces troops arrived and moved directly to the battlefield.

The displaced families arrived to safety carrying plastic bags filled with personal belongings. They had walked from neighbourhoods closer to the centre of the city. One family arrived on a donkey-drawn cart.

Across the street from where the displaced civilians were being loaded onto trucks, a wounded soldier was brought for treatment.

Later, the body of a dead soldier arrived. It was wrapped in a blanket bearing the image of Imam Hussein, one of the most revered saints to Shiite Muslims. Later, five members of the same family were rushed into the medical aid station. All five - a man and four children - were bleeding from shrapnel wounds when a mortar hit their home in the Tahrir neighbourhood.

Dozens of other displaced civilians also descended on the aid station but were turned away by troops, who said they had intelligence that IS was planning to send suicide bombers there masquerading as displaced families.

The progress of the Mosul campaign has been slow as the Iraqis and the US-led coalition avoid using overwhelming power against IS because of the presence inside the city of some one million civilians.

On Tuesday, a UN spokesman said the number of displaced people fleeing the military operation in Mosul has risen to over 68,000.

Stephane Dujarric said 8,300 Iraqis had been displaced from the city and outlying districts over the past four days, citing figures from the UN-linked International Organisation for Migration.

The majority of the displaced - 59,200 - came from the districts surrounding Mosul and the rest from inside the city, he said.